Estimating the bias in meta analysis estimates based on fixed effect model for data with missing variability measures - Nik Idris, Nik Ruzni (2012)
A common drawback with meta analysis is when the variability measures, particularly the variances , are not reported, or “missing” in the individual study. Among the approaches adopted in handling this problem is through exclusion of the studies with missing variances. Alternatively, the missing study-variances could be imputed. This paper examines the analytical implications of these two approaches on the overall effect estimate and the corresponding variances. The bias in these estimates are derived using the Fixed Effect model. The results show that no bias is expected in the estimate of the overall effect using both approaches. Similarly, there is no bias in the variance of the effect estimate when the missing study-variances are imputed and homogeneous study-variances are assumed across the studies. However, if the magnitude of the missing study-variances are mostly larger than those that are reported, imputation leads to under estimation of the variance of the effect estimate. This is a likely case in meta analysis. When studies with missing variances were excluded from analysis, the variances of the effect estimate are overestimated, and the magnitude of the bias in this case is relatively larger when compared to those from complete imputed data.